78.8.3 problem 3

Internal problem ID [18201]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 11:38:02 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 31

dsolve((2*x+3*y(x)+1)+(2*y(x)-3*x+5)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -1-\tan \left (\operatorname {RootOf}\left (3 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_{1} \right )\right ) \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 68

DSolve[(2*x+3*y[x]+1)+(2*y[x]-3*x+5)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [54 \arctan \left (\frac {3 y(x)+2 x+1}{2 y(x)-3 x+5}\right )+18 \log \left (\frac {4 \left (x^2+y(x)^2+2 y(x)-2 x+2\right )}{13 (x-1)^2}\right )+36 \log (x-1)+13 c_1=0,y(x)\right ] \]